Federal and state prosecutors charged Luigi Mangione this week in the killing of UnitedHealthcare’s chief executive in Manhattan, a two-pronged legal offensive that could complicate the high-profile case.

The Manhattan district attorney’s office charged Mr. Mangione with one count of first- degree murder, a terrorism-related offense; two second-degree murder counts; and weapons crimes. The U.S. attorney’s office for the Southern District of New York charged him with one count of murder, two counts of stalking and a firearms offense.

The maximum punishment for the state charges is life without parole. If convicted on the federal charges, Mr. Mangione could face the death penalty.

The state case is expected to go to trial before the federal one, said Edward Y. Kim, the acting U.S. attorney for the Southern District, and state prosecutors said they would coordinate with federal agencies.

Here’s what to know about the parallel prosecutions:

Are they legal?

Jessica Roth, a professor at Yeshiva University’s Cardozo School of Law and a former Southern District prosecutor, said there was precedent for federal and state cases to proceed simultaneously.

“It’s certainly happened before with respect to high-profile murder cases,” Professor Roth said, adding that the federal government has generally pursued its own prosecution when there were concerns about a state’s access to “sufficient resources or penalties.”